Measure of maximal entropy for minimal Anosov actions

2025/03/05 by Tristan Humbert, Humbert, Tristan
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2503.03457

openalex publication_date 2025/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a minimal Anosov \mathbb R^κ-action on a closed manifold, we study the measure of maximal entropy constructed by Carrasco and Rodriguez-Hertz in \citeCarHer and show that it fits into the theory of Ruelle-Taylor resonances introduced by Guedes Bonthonneau, Guillarmou, Hilgert, and Weich in \citeGBGHW. More precisely, we show that the topological entropy corresponds to the first Ruelle-Taylor resonance for the action on a certain bundle of forms and that the measure of maximal entropy can be retrieved as the distributional product of the corresponding resonant and co-resonant states. As a consequence, we prove a Bowen-type formula for the measure of maximal entropy and a counting result on the number of periodic torii.

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